For this type of installation, safety measures are usually provided by electric systems composed of, for example, electromagnetic locks which work with detectors, all of which are piloted by a control panel to which the various command circuits are connected. Generally, the complexity of these devices makes the cost of their purchase, installation, and maintenance prohibitive for private use. A way to make this kind of elevator accessible to private individuals consists in having all the functions performed by mechanical means, that are simple, reliable and only necessitate simplified maintenance. The motor function could, for example, be provided by a double extension jack and with constant speed like the one described in document FR 9311277 filed under this applicant's name. There remains nevertheless the safety issue, and in particular, being able to lock and unlock the doors with a simple mechanical device. The present invention is aimed at providing an elevator equipped with such a device.